Pump Affinity Law — Power vs Speed
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Power is head times flow, and head already carries a square, so power rides the cube of speed. Slow a 15 kW pump from 1450 to 1160 rpm — a mere 20% cut — and it draws 15 × 0.8³ = 7.68 kW, a 49% saving. That cube is why throttling a valve to reduce flow is such a waste: the pump still spins at full speed burning full power while you dissipate the surplus as heat and noise across the valve seat.
Two cautions temper the arithmetic. Real pump and motor efficiency sags at part speed, so the field saving is nearer 45% than 49%, and any static lift in the system means the pump cannot follow the cubic curve all the way down. Chilled-water plants still routinely bank 40–60% on pumping energy, which is why ASHRAE 90.1 has effectively mandated variable-speed pumping on larger variable-flow systems.
- = Power at speed 1
- = Speed 1
- = Power at speed 2
- = Speed 2
- Power at speed 1 — Fan Affinity Law — Power vs Speed, Pump Efficiency from Hydraulic and Shaft Power
- Speed 1 — Pump Affinity Law — Flow vs Speed, Pump Affinity Law — Head vs Speed
- Power at speed 2 — Fan Affinity Law — Power vs Speed, Pump Efficiency from Hydraulic and Shaft Power
- Speed 2 — Pump Affinity Law — Flow vs Speed, Pump Affinity Law — Head vs Speed